I’m working on a section of a game that teaches fractions. If a player misses the question about where to meet up with the returning hunter, he or she gets sent to study. There is a movie that plays before this about needing to get back to the camp before dark.

Here is the question,

“The sisters begin to worry their brothers won’t make it back by dark. They start down the trail to meet them. They decide to stop and wait at the spot where their brothers will be 3/4 of the way back to camp. How far FROM the camp will the girls be?”

trail

 

I used this question because I want students to think about a few ideas:

  • Distance between two points can be thought of as a whole.
  • If you are a/b distance FROM point X, the remaining distance TO point X is 1 - a/b  . Of course, I don’t expect them to state it like that.
  • 1/4= 2/8
  • Number lines can be numbered in either direction. You can have 0 on the left or 0 on the right. The distance will be the same. The size of each interval will be the same.

These are kind of important ideas in math – equivalence, the arbitrary nature of labeling points on a line.

Students can click on GIVE ME A HINT, and a hints page pops up that explains, among other things, why you were wrong if you answered that the sisters would be 3/4 of the distance to the hunting grounds FROM the camp. If, even after reading the hints, (or if they skip the hints and just guess, we’re talking kids, after all) they get the problem wrong, the player is sent to watch a video clip explaining the problem, and then has to take a quiz to get back to the game.

SO … I had the thought instead of writing the quiz questions out of thin air, I might read what some more experienced teachers were giving to students in this grade as math problems. After all, I haven’t taught middle school math since the 1980s.  I went to several sites, I even purchased some things like “One year of fifth-grade homework problems” etc.

When I looked at page after page of what students are being given as homework assignments, the only thing I could think was “Are you fucking kidding me? No wonder kids hate math.”

All of the homework was like this:

1/4 + 1/3 =   ?

For FIFTY problems. That’s it! Then, the next day, it would be another fifty problems like this:

5/6 – 1/4 =  ?

Okay, you need to learn to add and subtract fractions, but is that ALL you need  to learn? Obviously not. How boring must it be to sit and just calculate answers to the same type of problem over and over? This stuff made me start to hate math and I LOVE math.

How can you possibly think that is teaching kids math? That’s like making them copy down all of the words in the dictionary and pretending you taught them literature.

Don’t even get me started on teaching statistics – wait, too late. I’m started. That is my rant for tomorrow.

cake

I’ve spent a good bit of my life living and working in places that many of my colleagues would not drive through in the middle of the day with the windows rolled up and the car doors locked, so you’ll have to excuse me if I am a bit cynical about the latest push to teach everyone to code.

I’m not opposed to coding, in fact, I am greatly in favor of it. It is tied with drinking Chardonnay for favorite activity for which you do not have to get naked.  I was an industrial engineer in 1982 – so I was into STEM before STEM was even a thing.

What makes me roll my eyes and sigh is where many well-meaning people have completely missed the mark when they say that you don’t really need to know much math to write software. Clearly, they can’t mean all kinds of software because obviously if you write software to do statistical analysis, predictive analytics or whatever the phrase du jour is, you very much need math.

Often, these people are talking about games -

“Kids play games, let’s have them make them.”

That doesn’t necessarily follow any more than,

“I have a liver. I should create a dialysis machine.”

Ignoring the faulty logic for a minute, let me point out that most games DO require math. The people saying they don’t are usually people who are quite successful, both professionally and academically and have spent their entire lives around people much like them. What they mean when they say that, “Games don’t require much math” is

“I took three semesters of Calculus and a course in multivariate statistics and I rarely use any of that in making games.”

I, on the other hand, meet many people who can’t multiply two-digit numbers without a calculator and have never given a thought to the concepts of randomization, ceiling, floor or rounding. The vast majority of these people are perfectly intelligent enough to learn those things if ever given the motivation, time and instruction.

Here are a few lines from a super-simple game, “Canoe World”,  I wrote in the past two days. It’s a very common application. You can find it in the Game Design book by Rex van der Spuy and hundreds of other places. You randomly decide who is stronger, the player or “enemy”, one wins the exchange and points change  - a pretty standard game component.

function sink(thing) {
// The player’s strength ;
var playerStrength = Math.ceil((food+ health)/2) ;
var rockStrength = Math.ceil(Math.random()* playerStrength*2) ;
// Find out if the player strength is greater than the rock strength ;
if (rockStrength > playerStrength){
// The rock sinks the canoe ;
var lostFish = Math.round(rockStrength/2) ;
food -= lostFish ;
// Player gains experience ;
experience += 1 ;

 

To compute the player’s strength, I take the average of their food and health points, and round that up. That’s the ceiling function. To understand this, you must have some idea of order of operations – things in parentheses get done first – to understand that first I’m adding the two values and then dividing by 2.

You need to know that having that slash and then a number means to divide by a number.

That is math and not everyone knows it.

A ceiling function rounds up – and to understand that, you need to understand the concept of rounding.

To understand the second statement, you need to know what a random number is, that the * means to multiply. You also need to know that the random function generates a random number between 0 and 1 and realize that is a continuous distribution because there are an infinite number of numbers between 0 and 1.

That is math and not everyone knows that.

You’d have to realize that since the random number function is between 0 and 1, if you just multiply that number by the player strength it is ALWAYS going to be less or equal and the “enemy” will never win. Since, on the average, the random number will be .5, if you multiply by 2, that makes it equally likely the player or enemy will win and gives you a game of chance.

To change the probability of the player winning the exchange, you can make that number larger or smaller.

You need to know that the > means that the thing on the left is greater than the thing on the right.

All of that is math and not everyone knows it.

The people who want to teach kids to code assume that either,

a. Everyone knows this much math – in which case they are OH, SO WRONG!   or …

b. That they will work with the minority of students who do.

There is absolutely nothing wrong with option B. I wish you the best of luck with all my heart and will do whatever I can to help.

Most of what I can do to help is make games to teach math, so that more kids will fit with option B.

There is an option C, which intrigues me, and I have heard very few people discuss, which is to teach the math along with coding. That is certainly not impossible - but it would be hard – you would need students very motivated to put in the time and effort and teachers who were able to step back and start at whatever level of math competency required by an individual student.

This whole thing reminds me yet again of the comment made by Dr. Irv Balow, Dean of the UC Riverside School of Education. Frustrated by reading so much research that said under some conditions class size had an effect, under other conditions, not so much, for some students cooperative learning was a benefit, for others it was detrimental, etc. etc. etc. , a student asked,

“Isn’t there anything in education or psychology we know as absolute, unqualified fact?”

After some reflection, Dr. Balow replied, that the only thing he could be absolutely sure of was this :

“All of the simple answers are wrong.”

Having taught math myself for the past 30 years, and with a brother who is a middle school math teacher, I am obviously not tarring all math teachers with the same brush, but I am really starting to get pissed off here. I have beautiful daughters, and it is not just me who says so. Here is the oldest one.

Maria and Eva cuddled up

Here are the other three.

daughtersSee the middle one there? When she walked in for the first day of an advanced math class, the TEACHER (who was a woman), asked her,

“Are you sure you’re in the right class?”

Ronda came home and told me about it. She said,

Well, I guess I don’t really look like I belong in there. I’m the only non-Asian girl in the class, and I’m tall and blonde. I really stand out.

Ronda is extremely good at math. When she was young, we assumed she would get her Ph.D. in some kind of science, but she decided to go the UFC / movies route instead.

The other three could have been extremely good at math, but it was not a particular interest of theirs. The littlest one, on the left, has done quite well in math, until very recently.

What has happened with all of my daughters, though, is that the schools and I have generally butted heads with what we expected of them. When my oldest daughter met with the high school guidance counselor, and was asked what schools she was interested in, Maria said,

“I’d like to go to either Harvard or NYU.”

The counselor laughed and said,

Of course, everyone would like to go to Harvard or NYU but let’s take a look at the local community college.

I called the counselor up the next day and asked if she was fucking kidding me. I told her that her daughter could go to the community college, but if my daughter wanted to go to NYU or Harvard that is god damn well where she was going to go. Maria did graduate from NYU, in 3 1/2 years, thank you very much, when she was 20 years old.

Of my three older children, one has a bachelors from NYU, one has a masters from USC and one is finishing filming Expendables 3 this week and then flying off to film Fast and Furious 7. They are a fairly accomplished group.

And yet … more often than not, I was pushing them academically more than their teachers were – and you can’t find a much more yuppie school district than Santa Monica-Malibu, and most of the time they all went to private schools.  As a general rule, if they fell behind (which in my mind is anything less than an A because, seriously, what do they have to do but study? It’s not like they’re working in a coal mine after school or cleaning their rooms or anything.) – I was much more upset about it than their teachers were.  They did not EXPECT my children to make straight A’s, take AP Calculus, get into top schools.

When Maria walked into Geometry in the ninth grade, one of the girls she had run cross-country with the year before, who was a junior in the same class, exclaimed in shock,

“You’re smart?!”

Yes, one of my daughters was a cheerleader. Two were very much into sports in high school. Two were very much into going to the mall and buying every item of designer clothing sold in America.

If you are a math teacher, honestly, ask yourself do you have the same expectations for every student in your class? Really?

I asked myself that same question several years ago. I teach graduate-level statistics and I used to encourage the students “who I thought would be interested” to present their research at conferences, to publish it. I quit doing that. Now, I make those announcements in class, repeatedly, and encourage everyone.

Year after year, students have surprised me by the level of motivation and the quality of their work.

Honestly, if you teach AP Calculus and you have a pretty blonde girl that comes to your class some days in a cheerleader outfit (because that’s what they wear on game days), and is making a B or C, do you assume that is the best she wants to or can do? Honestly? Just between you and me?

One of The Spoiled One’s favorite movies is Legally Blonde. You know why? Because everyone assumes the protagonist is dumb because she’s interested in fashion, pretty and naive. In the end, she is dissuaded from dropping out by a professor who tells her that she can  do it, and the movie ends with her graduation from Harvard Law School.

If you’re a math teacher, I’d like you to watch that movie, because my kids DO live in southern California and they DO shop in Beverly Hills and contrary to what you think about how they look, they DO belong in your class.

 

If you want to be a programmer, entrepreneur or a statistician, the best advice that I can give is,

“Don’t believe other people are smarter than you.”

Sometimes that is hard advice to take. I read an interesting blog post by Ali Berlinksi, “I miss being stereotyped”, about being Asian-American and moving to an area in Spain where people had met so few Asians that they had no stereotypes. She said she missed the advantage of having people just assume she was studious, intelligent and good at math.

Of course, as she notes, most stereotypes are not nearly so benign. Many groups – Native Americans, women, Hispanics – are assumed not to be as good in math, or programming or really not the start-up type. Not many people say it that bluntly any more.

Last week, I happened to be in a seventh-grade math class at a predominantly Hispanic school, I asked,

“How many of you would like to be a programmer or design computer games?”

One girl’s hand shot up while the rest of the students looked at me (and her), as if it was a crazy question. I persisted,

“Why not? Seriously, why not? “

This wasn’t a remedial class. The math the class was doing when I walked in was closer to eighth-grade level than seventh, and remember, the school year just started. It’s often more a lack of encouragement rather than being actively discouraged.

My friend, Hayward Nishioka, is a phenomenal judo instructor and competitor, author of several books. We were having lunch this week and he said to me,

“You know, you need to give young people permission. You say to the student, you know, YOU could earn your black belt, YOU could become an instructor, too. You have that ability. Then they go ahead and do it, because you have given them that permission.”

I’m not sure that is true of everyone. Some people telling them they can’t it just makes them more determined. But, he is correct about a lot of people. He’s also correct that it is harder to keep going when you don’t have a lot of confidence you will succeed.

Programming is one of those things that takes a lot of perseverance – why do you think they call it hacking? It’s easy to get discouraged when your first attempt doesn’t run – and believe me, once you get out of CS 101 and get into real problems, your first attempt almost NEVER runs. Sometimes your second, third and eleventh don’t either. It happens to everyone. It’s normal.

What I’m afraid I see in too many classrooms, though, is that students have not been encouraged to believe they will succeed in the end or that that math and programming are things they should expect to be able to figure out. So, when they have that fifth failure, they just assume they aren’t smart enough.

Here’s another piece of good advice. Check out github.com – a place where you can find a generous number of code examples (and I feel terrible guilt that I have not contributed – although it is written on my whiteboard as one of the ‘must get around to’ items). When you are first learning a language, it’s great to see finished examples of  ‘the big picture’. Reading books on a language is great, but no substitute for actual working on a project. For me, starting with something like programming a tip calculator is as boring as watching paint dry. I’d rather jump in there and do something like a game. With github, you can read through examples and see where what you are learning is being applied.

Not everything on github runs or works as desired. People put up projects for review, projects that are in progress. As you gain more experience, you might want to download a project that is similar to what you want to do and just modify it. You’ll certainly see code that you would have written differently. You’ll see code where it is obvious that the person who put it up actually just downloaded it from somewhere and modified it, because there are modules, functions, that don’t really do anything — they’re left over from whatever the original program was. That’s your first insight into no, not everyone is smarter than you.

The nice thing about github is you can kind of lurk anonymously and look over other people’s shoulders and see that  no one else is perfect either.

As you gain even more experience, you’ll eventually start downloading code that you think, “Hey, I could do this part better. …”

Someone told me, no one has math anxiety, they have dumb anxiety – they are afraid that other people will think they’re dumb. This is another thing that github may help you with. I’ve never once looked at anything, and thought, “That person is really dumb.”  More likely, I’d think, they must be new to programming.

On occasion, I’ve downloaded a program from someone who had a reputation as being really smart, and found ways to improve it, for my purposes anyway. Did I think, “Wow, I must be smarter than that person”?

Not even once. What I actually think is, “This saved me a couple of days work and I really feel good that I can improve on something someone this smart wrote.”

So, my two points, before I toddle off to bed with a glass of Chardonnay:

1. Math, statistics, programming – you can learn it. Just start and keep going.

2. Github is awesome.

 

Let’s face it, 90% of everything on the Internet is crap.

Yelling childThis is especially true when it comes to educational resources.

So I cannot believe I did not come across these until now. Maybe they were just lost in the swamp of effluvia.  I came across so many good resources lately that I am planning on re-designing my course next spring to include a lot more applets, videos and other cool online options.

Here are some sites in the “Dude! You have to check this out!” category

Against all odds – statistics videos created in 1989! These are 26 half-hour videos on different topics on statistics. Think Nova for statistics.

Yummy Math – a website of activities making mathematics relevant to the real world. That’s their tag line. I’d say they make mathematics INTERESTING, like figuring out your savings buying Christmas presents, or comparing the durability of twinkies and tomatoes through time lapse photography or computing how much coffee could fit in a giant coffee cup. Go there. See for yourself.

SAS Curriculum Pathways – an enormous free site that has an unbelievable amount of stuff on statistics, algebra, geometry – oh, yeah, and I guess English, Spanish and Social Studies, too (if you care about that stuff). I have no excuse not to have looked at this before because I have been hearing about it for years and the nice people from SAS sent me links which I never clicked on but just sent to friends of mine teaching  middle school and high school. Hey, I’m busy. That’s no excuse. The school where I volunteer has a shortage of textbooks. Well, this site has pages to read, then research questions, then statistical applets.

Not strictly set up as an educational site, but Policy by the Numbers blog is like my twitter stream but far more in-depth. Posts on open data, Google hang-out on AP statistics. It was educational for me. Made me want to teach high school AP statistics. Just listening to this one video gave me two new books I want to read as possible textbooks for my class, so it’s educational for me.

The mathalicious blog is really cool. Their site also seems to have some good activities based on the sample ones but I’m not sure because they want $185 a year for a license, which strikes me as a bit steep.

Last but definitely not least is CAUSEweb.org – which I had actually seen before but I guess I was busy (detecting a pattern here?)  This is the Consortium for the Advancement of Undergraduate Statistics Education. The first thing I saw here was a free workshop in San Diego on playing games to teach statistics, funded by a National Science Foundation grant. I signed up for it on the spot.

It’s been a very productive week for finding sites and other resources I want to review for teaching statistics. So much so that I used this other site, 43things.com to make a list of all of the stuff that I want to consider for the grand-a-mundo course re-design.

Please, please, please if you have suggestions, chime in.

 

 

hunter-on-horse

Here is a math problem:

Hoksinato and Tasunka Ska are going to steal horses. They could steal the scrub ponies from the edge of the camp. The last 15 times warriors from the tribe tried to steal scrub ponies, they got away 12 times and were caught and tortured 3 times. If they steal the war ponies instead, they will show more bravery, maybe even earn an eagle feather. Plus, war ponies are much more valuable. The last 10 times warriors from the tribe tried to steal war ponies they got away 3 times and were caught and killed 7 times. What is the probability that they will steal the war ponies and get away?

The correct answer is 30%, in other words, 3 out of 10 times.

Another way you could possibly answer it is 12%. You could interpret it as there were 25 attempts at stealing ponies, and that the question was,

What is the probability that they will steal the war ponies AND get away?

In that case, the probability is 40% that they will steal the war ponies (versus the scrub ponies) and 30% that they will get away, .40 *.30 = .12

Thinking about this, I decide to re-word the question. To say,

Hoksinato is not sure whether or not they should try to steal the war ponies. What is the probability that warriors stealing war ponies will get away?

A statistician would immediately think of this in terms of P(A|B)  in other words, what is the probability of escape given that they are stealing war ponies? The answer is clearly 30%.

Here is why solving this problem is hard

  1. It is not worded to be completely clear whether I need to know the probability of getting away when stealing war ponies or the probability of getting away AND stealing war ponies.
  2. I need to decide which numbers are relevant. For this particular problem, the probability of escaping when stealing scrub ponies is irrelevant.
  3. I need to decide on the correct operation, in this case, to find the percentage of successful war pony theft attempts, which I find by dividing ten into three.
  4. Finally, I need to know the answer to 3/10

Why don’t I just ask, “What is the probability of escaping, if a warrior escapes 3 times out of 10?” Because that is a much easier problem. Here’s the kick in the ass – problems in real life don’t come up that way. They occur ambiguously worded with extraneous information thrown in.

Many people, including most of those awarding funding at the National Science Foundation, realize this and thus very strongly urge mathematics programs to teach problem-solving via discovery learning, guided discovery or other methods. These people are right – to an extent. As you can see above, basic mathematics alone won’t solve this problem.

Many other people, including many math teachers at low-performing schools, believe the NSF is run by COMPLETE IDIOTS because the students don’t know the concept of probability, much less P(A|B) , they have no idea of the notation, where to even begin deciding which are the relevant numbers and oh, yes, they can’t divide 10 into 3 and come up with .30 either. These people are also right – to an extent.

If we are going to teach kids math effectively, we need to fund projects that bring these two sides together.

Y’all get on it.

 

 

It’s not often that you read a paragraph and it sticks in your mind for months. That this particular paragraph came not from some great literary work but rather from the proceedings of the annual meeting of the Association of Small Computer Users in Education is even more expected, but there it is. Douglas Kranch wrote:

“Expertise develops in three stages. In the first stage, novices focus on the superficial and knowledge is  poorly organized. During the end of the second stage, students mimic the instructor’s mastery of the domain. In the final stage, true experts make the domain their own by reworking their knowledge to meet the personal demands that the domain makes of them.”

This idea kept coming back to me in a lot of ways. I have a thirteen-year-old daughter who is now learning the basics of chemistry, algebra and physics. I teach students statistics, and often have them use SAS for data analysis. I’m in the middle of using javascript for a much larger scale application than I have created with it in the past.

Julia falling asleep over homework

I get irritated by the frequent use of  the phrase “STEM education” for science, technology, engineering and mathematics, as if there is no difference among organic chemistry, javascript and calculus, but in this case I really did see a common thread.

Existing mathematics (and statistics and science) education programs are too limited. They either focus ONLY on drill and practice, not progressing past the first stage, or they try to skip the first stage or two entirely, an overreaction that while having the laudable goal of teaching “higher order thinking skills” often leaves students frustrated and discouraged as they do not have the basis for the tasks required. Part of the problem comes from, I think, having subjects taught by people who were not experts themselves.

Let me give two examples, one horrid and one good.

It’s common for middle school teachers to give students assignments that are supposed to be “relevant”, for example, “Make up your own periodic table”. They did not, however, come up with a new way of arranging elements. No, they did a periodic table of football players or TV shows. I suggested to The Spoiled One that perhaps she could do Disney channel shows and have those that had a character move from one show to another be in one group, just like elements that lose an electron are in one group. Similarly, those shows that shared a character, like if Miley Cyrus also did appearances on The Suite Life could be a different group, like those elements that shared an electron. I was out of town at the time –  (if you follow this blog, you know that my children contend most stories of their childhood begin this way) – but when the project was due, the world’s most spoiled thirteen-year-old turned in something she drew with a pencil on a piece of paper and got a 50% on it. When I quizzed the rocket scientist about how this happened he answered unrepentantly,

“I didn’t make her put any effort into it because she said it was stupid and I agreed.”

While I did not have this precise conversation with the school –  Seriously… What. The. Fuck – you want a kid to learn about the periodic table, covalent and ionic bonding – you teach them that,  NOT relate it to stupid  TV shows we’d just as soon she not watch any way. We spent many hours going over with her the idea of electron shells, what happens when a shell is not full, the number of electrons in each shell. You want a kid to know that NaCl is sodium chloride? You explain that Na is the symbol for sodium and Cl is the symbol for chlorine and you put the two together and you get sodium chloride. There’s actually some really interesting stuff you can throw in there about how it’s kind of weird that when you combine these two elements you get something that really isn’t very similar to either one individually. You want to get kids interested in chemistry? Do experiments. Few things are more motivating to the average eighth-grader than the possibility (however slim) that they might get to see the school blow up with the teachers in it.

I’ve been a teacher. I started out, like most people, as a not particularly good teacher, and then, with years of experience, I got better. I recognized that all of that stuff, like the periodic table the electron shells, multiplication tables, how to read an ANOVA table, you need to learn that. Even if you don’t get it at first, if you ” … focus on the superficial and your knowledge is poorly organized” – you still learn that p-values, df, sums of squares should be in there. At first, you don’t know what df stands for and when you find it is degrees of freedom that doesn’t really tell you much. After a while, you vaguely start to get it. It’s frustrating, it really is, going through those motions you don’t really understand – but there isn’t any alternative.

Let me go on to a different example. I wanted to use javascript to write an extremely complex application. So I needed to learn javascript better. I read a couple of books. I did a bunch of codecademy exercises, watched some videos. I wrote small programs that did bits and pieces of what I wanted. Then, I took someone else’s program that was pretty complicated. Not thousands of lines of code but hundreds. I went through and typed in their whole program line by line trying to figure out what each part did as I copied it. After I got it to run, I made some changes just for my own amusement. Then I did the same with a few other programs.

After a while, I could see where those “master programmers” had made mistakes. I’d notice they’d left a semi-colon off the end of a statement, left out the period, typing Mathrandom instead of Math.random or used a semi-colon when calling a function instead of a comma. In short, I got better at understanding the superficial – how the syntax has to look. At the same time, though, I started to see how the logic worked.  To see how one could use a loop inside a function to draw a deck of cards, for example. In the end, I had a game that worked. Then I changed it to be a different game, more like what I had in mind. I’m not as expert as I’d like to be in javascript yet, but I’m getting there.

Yes, in this process, I drew a lot of connections to other programs I had written in other languages. What I did not do is draw a parallel with the time we got lost and went driving around Miami trying to find somewhere it was legal to make a u-turn. (Let me just say that Florida has commitment issues. If you are going south they think you should just keep going and if you change your mind and want to go north, forget it.)

What I also did not do is one mindless fill-in-the blank or multiple-choice exercise after another ad infinitum. I didn’t memorize rules until I could pass some arbitrary test at 100% accuracy. Although I did start with that, I didn’t finish with it. In fact, I did the very minimal amount until I could move on to the imitating experts and making it my own.

If you want to learn programming, statistics, chemistry then DO that. Don’t just read about how to do it and for the love of God, don’t do something else, like stupid charts of TV shows or biographies of women mathematicians and pretend you’re doing STEM education.

Daughter number 3The third of my four daughters was being questioned about her training before the last Olympics, and answered;

My mother was the first American to win the world championships, so I called her for advice, and believe me, Mom is always brimming with advice, whether you want it or not …

 

 

In fact, all parents have the experience that their own children occasionally take advice from strangers far better than from them. So, for your daughters or mine, here are three pieces of advice on succeeding in the tech world.

1. Learn Calculus – Ignore every person who tells you that you won’t need it, it’s too hard. Take it in high school and take it again in college.  People often say, “I just can’t do math.” That’s bull shit. You just can’t make the NBA. You can certainly do math. My youngest daughter whines that way sometimes and yet she doesn’t sit and read her Algebra book unless we stand over her and make her do it. Here is why you need to learn calculus:

  • 99% of all math books are written to be so boring that you want to track down the authors and bitch slap them. Learning calculus is good training for life because there WILL be boring things you have to do to get to where you want to be. By ten years old, you should have overcome the idea that everything has to be as intrinsically rewarding as laying on the couch with your puppy.
  • If you do happen to have a  hard time, even better. Don’t skip class. Read the textbook. Get a tutor. Read the book again. Everyone at some point runs into concepts that are difficult. This happened to me twice, in calculus and in my fifth semester of statistics in my doctoral program. Now, in both areas, it is hard for me to understand why it was ever confusing, but I remember at the time reading the book over two or three times and still being a little fuzzy and afraid I wouldn’t ever get it.  I’m married to a real-life rocket scientist, a man who decided to pursue a Ph.D. in particle physics because “nuclear physics was too easy” and even he had a point in school when he ran into concepts he had to read over and over until he understood it. Find a way through. That’s a super-important lesson in  life.
  • If you learn calculus, you WILL use it. I took Calculus I & II my freshman year of college. It came up in a few economics courses my senior year and in my first statistics course, which I took in the math department. I never had any use for calculus for years after I graduated. Then I went on for a Ph.D. and specialized in Applied Statistics.  Calculus was really useful in some of those courses. Now, in my profession, whether reading research, reading documentation or programming, it comes up fairly often. Not every day, but certainly every month.

2. Learn to say “Fuck you” and say it both openly (rarely) and to yourself (often).

My friend has a reputation for a great bedside manner. He uses a code phrase. When a patient says something like:

“I have decided to treat my cancer with grapefruit juice instead of chemotherapy.”

He responds,

“I understand how you can see it that way.”

This is his code for,

“You’re a fucking moron.”

You need a code phrase because people will try to dissuade you, denigrate you and generally provide useless advice (contrary to the wonderful advice I am giving you now). They will tell you that you cannot be an entrepreneur because you want to have a family. They’ll tell you that you are not a real ‘techie’ because you don’t have a degree in engineering. If you do have a degree in engineering it will be because you don’t have a degree in Computer Science. If you do have both degrees and have experience as an engineer and programmer it will be because you don’t know a specific programming language. Some people seem to have a sadistic desire to pull other people down, saying things like,

“You may have a masters degree but it’s not computer science from MIT. You don’t program in Ruby or Java and everyone knows that unless you have years of experience in both of those you are not really marketable.”

Feel free to tell those people, either:

“I understand how you can see it that way, but I’m going to go ahead and apply for the position at the accelerator anyway.”

or

“Fuck you! I’m going to do it anyway and I don’t care what you think.”

Seriously, there are very few insurmountable obstacles. One of my daughters received a Fulbright scholarship to study in Germany for a few weeks. She almost didn’t apply because she had a young child. I told her that she was being ridiculous, she had a husband, a mother, a mother-in-law and two adult sisters. Between the lot of us, we could take care of one baby.

So what if I let her teethe with Twizzlers during the week  I was there?

I also took her swimming in the hotel pool every day, to the science museum, to the aquarium and taught her to dance in elevators. And when Maria came back from Germany, her daughter was still alive, better than ever, because, hey, she had a couple more teeth.

This is really the most important piece of advice I have. Don’t let anyone discourage you and that includes yourself.

3. Learn a programming language or two.

If you followed my first two pieces of advice, this third one will be easier. The whole trick to learning a language is to not get discouraged and plug away at it. Read a book. Write some code. Read another book. Look at programs other people wrote. Think of some things you want to do with that language. Try them. Fail. Swear. Try again. Don’t get discouraged.

Douglas Kranch gave a good description of how expertise develops,

” Expertise develops in three stages. In the first stage, novices focus on the superficial and knowledge is poorly organized. During the end of the second stage, students mimic the instructor’s mastery of the domain. In the final stage, true experts make the domain their own by reworking their knowledge to meet the personal demands that the domain makes of them. “

This is why those first two bits of advice matter. In learning programming it is easy to get bored or discouraged as you go through those first two stages. It’s easy to start believing it’s too hard, that guy who told you women don’t have the same natural talent for programming was right, it’s too late for you to start now because you didn’t take enough math in college …

“I understand how you can see it that way.”

I was very busy this weekend working on the semi-annual site update (I am SO getting last place in the Search Engine Optimization contest) and starting on my book – Beyond SAS Basics: Tips, Statistics and a Naked Mole Rat and on TOP of all of that, I had to take the world’s most spoiled 13-year-old shopping because there are apparently some items of clothing and footwear existing in Santa Monica that she does not own yet.

Unhappy camperI’m also working on a proposal for math education software and I got to thinking that there is SO much out there, how can there possibly be the need for any more. In (very) partial payment for the shopping spree, I had The Spoiled One review math games and websites for me. Since I don’t see the need to call out any particular resource just because she happened to randomly land on that one today, the names have been omitted to protect the guilty.

As background, I should tell you that she was recently accepted for a summer program for high-achieving girls, scores above average on standardized tests for math (not as above as WE would like) and has never made a grade below a B in anything. (Because in our house a C means you are grounded until the next report card.) On the other hand, homework is sometimes accomplished only as a means to effect the return of all of her confiscated electronics. In other words, she is a little better on achievement and motivation than the average student, but hardly a paragon of mathematics virtue. And here were her reviews:

 

Video of Rap Song on Mathematics Topics (Because, you know, you kids these days like that)

… Um, distracting. I learned nothing because I couldn’t understand the lyrics.

Place Value Video Lecture

Not really for someone my age (13). Kind of stupid anyway.

Pre-Algebra Game

Sucks! (She drew a picture here to indicate how much she hated it.) BORING. Doesn’t really work. (Punctuated by another picture)

Game with Word Problems

The game was good I guess … (a few minutes later…. ) Never mind. It didn’t give you the right answer after. I HATE THIS SITE.

Game on Factors and Multiples

OK. Not creative or fun. (Another picture, that looked something like this

  • . .
  • |

Sites on Math in Every Day Life/ Real Life Math

Eewww  NO!!  Doesn’t make me like math!

Mucho Math- The only one that didn’t suck

“That one with the Hispanic math teacher and the kid. That one was okay and kind of funny even though the topic it was on wasn’t really at my level.”

I found this last comment extremely interesting because I knew who she meant. I had sat my daughter down at a computer on a web page with over 1,000 videos, games and other math resources and she came up with the same option that I thought was one of the best ones I’d reviewed when I was doing  the same thing a couple of months ago.  The teacher is Lawrence Perez. The innovation he has included is really quite simple – he has a student in his video.

Having reviewed numerous other options myself, I have to say I agree with my daughter on much of it. The absolute WORST thing you can do in designing mathematics software is have it get the wrong answer, for example, when it asks :

If Y = 5 + x**2    and Y = 14    what is X

and you put  -3   and it says

WRONG!  The answer is 3

Of course, -3   is also a valid answer and then you have a student who says,

“I hate this program. It sucks!”

Not as bad, but also frustrating are those programs that don’t tell you the answer, but simply come up with the next question.

If you say that both of these problems are examples of poor design, well, I agree with you, but poor design seems to be rampant.

Having a game or video that is too basic is not the problem of the software, of course, but MAYBE whoever marketed it as being at the middle school level. Or, it may just be that there is wide variation among students and was not appropriate for this particular student.

Yes, I’m generalizing from an N of 1 (well, 3 actually, if you include me and my brother, who is a math teacher and has had generally the same responses), but from what I have seen so far, there is a whole lot of math education software out there that is not effective in interesting students enough to use it. Sometimes the game doesn’t even do the minimal job of providing the right answer, something any parent could accomplish with a $1.29 stack of index cards by writing the question on one side and the answer on the other.

Every time I have done this experiment, whether with me, my daughter or someone else, the outcome has been equally underwhelming. Even more underwhelming is the fact that almost NONE of the designers/ producers of these resources even MENTION the thought that perhaps one would evaluate  the software and see if it has any impact at all. The attitude seems to be “Here you go”.  Period. Kind of depressing.

I guess the good news is that there are about a bazillion more games, videos and other resources out there to try.

I’ve been reviewing a number of options for students to learn mathematics.

A lot of sources kind of sucked. At best, these sites were just the same old thing, flash cards but on a computer screen, for example. There is nothing terribly wrong with that, but it is hard to imagine that they have any greater benefit than just using index cards you picked up at any store and writing 2 x 3  on one side and 6  on the other, which is how I think everyone has learned multiplication since we quit writing on slates with a piece of chalk. Hey, maybe we should go back to that. It probably involves less waste. Green math! But I digress …

At worst, these sites were just plain wrong. This was more often true for those that dealt with less basic mathematics, where they would, for example, give a definition for a chi-square that was really for a t-test or say that the median was the most common score in a distribution (It isn’t. That’s the mode.)

 

Other sites were better, including videos of short lectures and the explanation of whatever the topic they were teaching was correct. (AnnMaria’s first rule of teaching – have something non-stupid to say).

Two examples are:

  • Khan Academy site, which is free, has over 2,000 videos and Bill Gates as its BFF.
  • Cool Math Guy website has some free samples, for others, you have to pay. The videos I saw are good explanations of such topics on trigonometry.

There are hoards of math game sites out there, many of which are just a computerized version of asking your child over and over what is 47 + 52 until his brain crawls out his left ear and runs away just to escape the boredom.

Then, there are sites like Gamequarium, which offers a LOT of different math games for every topic, most of which look like they would be fun if you were immature, which I am.

ALL of the resources I found suffer from the same fatal flaw which is that they begin with the presumption that the student has some interest in learning math. This seems a reasonable, some might even say ‘sane’, assumption based on the fact that the person has come to a site that is for teaching mathematics. For those people who seek out these sites, they might work.

The problem is with the vast majority of people who WON’T ever voluntarily go to these sites because they really don’t give a rat’s ass if they ever learn math or not. Sometimes, as this excellent article “The Education of Jose Pedrazza” points out, they are much more concerned about whether they are going to be homeless, how their family is going to eat.

Given those circumstances, it’s really hard to focus on if you learn this math, you’ll be able to do next year’s math and so on for the next 10 years until you graduate from college and get a good-paying job. It’s all well and good to talk about delayed gratification when you are sitting here like me drinking Chardonnay at an expensive oak desk, and quite another when your mom is collecting cans to come up with money for dinner.

Some of it, the odds are great that you will NEVER use. I just came across this statement in a publication on research in teaching and learning mathematics.

“Across all age levels, the best estimates are made in temperature situations and the most difficult estimates involve acreage situations.”

ACREAGE? Okay, I’m 52 years old, I use math for a living, I’ve bought and sold four houses in my life, including one that had five acres of land with it and was in North Dakota AND NEVER IN MY LIFE HAVE I NEEDED TO ESTIMATE ACREAGE!!

Yes, I am sure there are farmers and landscape architects and people doing surveillance for homeland security applications who may need to estimate acreage. Every  time I write something like this, I get hate mail from people telling me this is why they will never hire me to work for them at Google Maps. (Of course, when I look up these people, they never actually work for Google, or anybody. They are invariably some embittered graduate student teaching Mathematics of Acreage Estimation at Boo-hoo U. )

My point is that most of math is taught completely out of context with no real thought to application other than answering a question on the SAT. For some students, like the most spoiled 13-year-old in America, who happens to live in my house, that is adequate enough incentive. One reason is that for her, and many of her peers, it is NOT gratification delayed ten years. At the end of the school year, many neighborhood parents trek to the Apple Store to buy the iPhone 4 or the gadget du jour for Buffy and Justin who got an A in math. In eighth grade, the kids will all take their high school entrance exams, and when the test scores come and acceptance letters come out, there will be ANOTHER round of iPhone -buying and trips to The Grove. A couple of years after that, many of those same kids will get  their first car, with the stern admonition that, “Your grades better stay up or you will be walking to St. Alphonso’s Catholic High School “.

I was a little depressed after I read this article on the Los Gatos Patch, where the mother happily admits that she could not do her 14-year-old son’s Algebra class. It tells me not only that we find it perfectly acceptable not to know math (while it is NOT okay to say that you forgot how to read) but also that the mom obviously has no need for Algebra in her daily life. On the other hand, I was majorly impressed that she got her son to make dinner and to clean up – twice.

Some people just like math – I did and I still do. That’s only incentive, though, to study the parts that interest you. For example, I watched a video on trigonometry for about five minutes. Then I was bored. It was exactly like the movie, Freaky Friday, where the middle-aged mother changes bodies with her teenage daughter, and in algebra class tells the teacher, “No, believe me, I will NEVER use this.”

I use algebra nearly every day of my life. I use matrix algebra, not every day, but certainly weekly, and calculus fairly often, too. On the other hand, I have NEVER and I do mean, NEVER, needed to know a sine, cosine, tangent, arctangent for any reason whatsoever, not even when I was an industrial engineer. This isn’t to say that no one ever uses these. I asked the house rocket scientist when was the last time he used any of these and he said that everyone in the real world uses all of these every day.  Well, EXCUSE ME!

Perhaps we have it backwards. Instead of railing about the poor performance of our kids on tests and teaching to the test, maybe we should turn things around. Perhaps we should start with why they need to know how to calculate acreage, t-tests or cosines. Give them some projects where this information as applied. Maybe then not only will they actually give a rat’s ass if they learn it or not, but they’ll also still remember it when they have 14-year-old kids of their own and be able to use that information on the job when people like me hire them.

Wouldn’t that be a nice change of pace?

 

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